Can't download macOS Big Sur 11.5.1

There are several ways to download the Big Sur 11.5 update. 

1 - Connect to Router via Ethernet connection and restart the computer in Safe Mode and then open the Apple Apps Store and get the Full Installer of Big Sur. It will be the 11.5 version and once downloaded run the installer from the Applications folder.

2 - Resart the computer in Recovery Mode ( INTEL Command + r ) and choose Reinstall macOS. It too will download the full Installer and commence the installation. For M1 CPU the Recovery Mode is Here

3 - This method may seem unnecessary but sometimes the Router Restart clears Network issues from ISP to Apple Servers

Shutdown Router. Shutdown computer and disconnect all External Drives. Restart Router. Connect to Router via Ethernet Cable. If via Wifi - Disconnect all other Devices using the Wifi - want the Maximum Bandwidth only for this computer. Restart computer in  Safe Mode. It does a Repair Disk, Clear System Cache files and only load Apple Software, extensions and Fonts. Will load slowly - Normal. Once Logged in - open Apple Apps Store and  Get the Full Version of Big Sur. It will take some time and several pauses will occur - normal. Countdown clock may say 15 minutes but in Real time may be 30 minutes. Same goes for clock at 10 minutes could be 20 minutes in Real time. Eventually , Full Installer will download and a New Application in Applications Folder will present called Install Big Sur. Stop there and perform a Time Machine Backup. If desired - have an External Drive - Copy & Paste the Install Big Sur Application to external drive for future usage - making a Bootable Installer. Now run the Installer.

Have found this method more reliable than the Software Update which is very iffy at best

Are you using WiFi to download, always best to use a cabled connection to your router when downloading

from Apples Servers. If you can only use WiFi then have your mac as close to your router as possible.

Do not use the mac while it is downloading and do not use any other devices that share the same

internet connection.

15GBs of free space is not very much, aim to have at least 20GBs of free space more is better this is to

allow your mac to perform its own housekeeping, running a mac with little free space could cause it to

lock up and become unusable.

Although it has installed successfully - the computer appears to be running out of Empty Space ( as per the posting above ).

Must caution you, good computer practices are to ALLWAYS have at least 15% of the drive empty. Leaving lest is going to degrade performance, over tax the CPU and Memory and other unexpected things can happen. If left too long and not actioned soon, it could even stop booting at all.

Suggest inventorying what is installed, what is required to function and discard the unneeded.

Use wrote " DOWNLOAD FAILED - An error occurred while downloading the selected updates. Please check your internet connection and try again. " The problem had nothing to do with my internet connection.

Thanks Apple for such a misleading error statement... "

Agree the initial Error Message is misleading and Cryptic. But, at the same time was an Alert that something on the computer was not correct. As you discovered, it was a Lack of Empty Space.

In retrospect, it was a good thing 11.5.1 did not install or you might have come back to these ASC Forums complaining Apple had bricked my computer